Every physicist should know that frequency and time are complementary variables. They’re related by an uncertainty principle, similar to the uncertainty principle in quantum mechanics governing position and momentum. The more precisely you know the position of a particle, the less precisely you can know its momentum. The more precisely you know its momentum, the less precisely you can know its position.

Likewise, if you want to precisely know the frequency of something, you have to average over a long period of time. If you want to know how the frequency changes over short timescales, you must accept an inherent uncertainty in the frequency.

One of the ways in which people are different from each other is in how frequently they’re sexually attracted to other people. However, our sexualities are not always constant throughout our lives. Therefore, you can describe (one aspect of) sexuality with a frequency, and you can say that this frequency changes over time.

But there’s a fundamental limitation to how precisely you can know frequency and time together. If you want to talk about how someone’s frequency of attraction varies from year to year, then it is impossible to pin down this frequency with precision greater than once a year.

Mostly, this doesn’t matter. If you’re attracted to about ten people a year, then what does it matter if you’re not sure if it’s actually nine or eleven people a year? Who can even count up that high anyway?

However, if you’re very infrequently attracted to people, and experience high fluidity, then we enter what I’m going to call the quantum sexuality regime. Here, the fluidity uncertainty principle reigns.

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About Siggy

Siggy is a physics grad student in the U.S. He is gay gray-A, and makes amateur attempts at asexual activism. His interests include godlessness, scientific skepticism, and math. While not working or blogging, he plays video and board games with his boyfriend, and folds colored squares.

11 Responses to The fluidity uncertainty principle

This is a bit of a tangent, but on the subject of “quantum sexuality” – I’ve jokingly used that phrase before in critiques of the somewhat annoying belief that asexuals and bisexuals are only “queer” if they’re in same-gender relationships, and they’re not queer if they have opposite gender relationships – if we take this as true, it leads to the assumption that a single person must have some sort of “quantum sexuality” that is both queer and not-queer at the same time and only settles into one or the other when it is observed in the context of a relationship.

This is an interesting idea, but I don’t know how accessible the details are to those uninitiated in Fourier Analysis. You know what would clarify things? More maths.

Content warning: Maths, pleonasm.

(Paragraphs in parentheses are asides and may be skipped without affecting the central points.)

Before I get into developing this concept, here’s a somewhat interesting caveat: this analysis does not apply to the “strictest” definition of asexuality (by which I mean someone who clearly experiences no sexual attraction to anyone ever). This is because our definition of uncertainty refers to a normalizable distribution, one for which we can define a basis-independent Parseval intensity functional. But in the case of a trivial distribution (i.e. always 0), this does not exist. Basically, it’s a divide by 0 error.

It is also important to keep in mind that we’ll be concerned with the frequency of an event, not the question of if it is frequent. Someone who experienced a strong, constant state of sexual attraction would frequently experience sexual attraction. But the frequency of this attraction is 0, since the level of attraction does not change.

To make this clearer in the following analysis, let’s ignore the intensity of attraction, the number of subjects of such attraction, and any ambiguity to this state. Instead, we just treat attraction as a Boolean variable. One is either sexual attracted (f(t_1)=1) or not (f(t_2)=0). f(t) is a series of step pulses (times when f(t)=1) separated by various intervals (when f(t)=0).

To make this even more concrete, we’ll consider the case of monitoring the presence of sexual attraction in one’s own life. I take that distinction for two reasons. One, one can constantly perform this monitoring (that is, f(t) is continuous), and two, constantly charting someone else’s sexual attraction seems creepy. This monitoring is assumed to have gone on for some time period T, which can be since your earliest memory, the onset of puberty, that time you volunteered to only eat aphrodisiacs for science, whenever. When we Fourier transform f(t), we will be left with a sequence of numbers indicating what frequencies were present and their relative influence. These frequencies will be in harmonics of 1/T (this is exactly like harmonics in music, they’re just 1/T times a whole number). The longer you’ve been monitoring, the longer T will be, and therefore the shorter 1/T. This will increase the resolution with which you can specify the frequencies that compose f(t).

What the time-frequency uncertainty principle says is basically that, the more you localize something in time, the less well-defined it’s frequency will be and vice versa. This is relevant to questions one might ask like, “Given that I’m currently experiencing a (lack of) sexual attraction, how long will this likely last?” (this is limited by uncertainty in time (and the problem of induction, but let’s not get into that)) or “how regular/random is my pattern of switching between experiencing and not experiencing sexual attraction?” (this is limited by uncertainty in frequency). These seem like the sorts of introspective questions that anyone might ask, regardless of their specific experience of attraction/fluidity.

(So yes, “if you want to precisely know the frequency of something, you have to average over a long period of time. [Otherwise], you must accept an inherent uncertainty in the frequency.” (For reference, precision is just how much one can say about a measurement – it’s related to the number of significant digits and the size of the error/uncertainty. It is different from accuracy, which is how well an observation matches reality) But this is not equivalent to, or indeed implies that, “If you want to talk about how someone’s frequency of attraction varies from year to year, then it is impossible to pin down this frequency with precision greater than once a year.” The harmonics measure variations on shorter time-scales than the fundamental frequency 1/T, so this does not follow. And the longer one extends T, the more precisely one can specify frequency. Problems also apply to an unqualified claim that “you can describe (one aspect of) sexuality with a frequency, and you can say that this frequency changes over time.” Fourier analysis is not good for defining a time-varying frequency. It is only really useful for time-scales where the frequency composition is relatively stable. For example, the linear chirp, \sin(\Omega t^2), has a linearly increasing frequency over time, but this is not reflected in Fourier analysis. One could separately apply Fourier transforms to various periods of time, and this would let you monitor how the dominant modes change over time. But the limitations of choosing this method of binning time are different from the general limitations of Fourier transforms.)

Lastly, a word on modifying my model to include some of the previously ignored complexities. Ambiguity can be incorporated most readily by either allowing attraction to take on real values or by imposing fuzziness in the specification of levels of attraction. Intensity/number of attractors can be incorporated by allowing attraction to be greater than 1. Removing the constraint of constantly monitoring attraction (in case one is lazy or creepily monitoring someone else on a regular – but not constant – basis), f(t) would become discrete and there would be a limit to the precision with which we could specify frequencies (in particular, the sequence of frequencies used would now be finite and we’d have to worry about things like aliasing). These modifications do not affect the frequency-time uncertainty principle, which is a general consequence of trying to describe a system with conjugate variables.

(Another amusing example of how frequency and frequent are different. For the Boolean attraction model f(t) given here, one could also describe the Boolean attraction of one’s sexual evil twin, g(t)=1-f(t), or the attraction experienced by a person who only feels sexual attraction why you don’t. Assuming that neither you nor your evil twin are Parseval trivial asexuals, then you both have the same frequencies and Parseval intensity (except the constant mode) describing your sexual attraction.)

I’m glad someone took my quantum sexuality theory literally rather than merely as an analogy, although I think it mainly demonstrates the limitations of the theory.

You can characterize people with a function f(t) = (number of people attracted to at time t), but if we do this, it seems strange to identify the asexual spectrum with the dominant frequency of f(t). If someone has f(t) = 1, the only frequency mode is zero, but it seems strange to call such a person asexual, since they are always attracted to one person. I was imagining was that f(t) is more like a counter. It has a brief pulse every time you’re attracted to someone new. If f(t) were a sound wave, someone’s frequency of attraction would correspond to the perceived pitch. But we can hear pitch change over time, and that’s fluidity. (I don’t know much about how the ear works, but presumably it does some sort of fourier transform with a shifting window.)

How would one include other aspects of sexuality besides frequency of attraction? Probably the easiest way is to start by ditching the f(t) analogy.

So this proposal is by no means complete, but here is how I would begin tackling a model.

Let us consider a collection of people. Each person will be associated with a (vector-valued) function g(t) which denotes their instantaneous gender expression (vector valued to allow for non-binary identities. And expression because that’s what other people can perceive).

People can be linked by various interactions/attitudes, but for now let’s just consider sexual attraction. Person (i) will have an attraction table a_i(t;j), which is the instantaneous attraction that person (i) experiences to person (j) We can now think of this system as a graph. People are nodes linked by (directed, since the attraction of (i) to (j) is not the same as (j) to (i)) edges denoting attraction. More precisely, let us say that edges are formed when people meet (we’re ignoring fantasy and similar complications right now). Attraction is some arbitrarily graduated function, the exact measurement and graduation is not addressed here.

To categorize person (i)’s sexuality is to characterize a_i(t;j) for all (j) and t. There are a number of things that could be addressed. First, we could look at the correlation of a_i(t;j) with g_j(t), that is how person (i)’s attraction to person (j) varies with (j)’s gender expression. Averaging over all (j) would then give distinctions between sexual orientation.

Second, we could look at correlations of a_i(t;j) over time. In particular, we want to distinguish if a_i(t;j) starts high and remains there (sexual), starts low and goes high (demisexual), starts low and remains there (asexual), or starts high and goes low (I don’t know if this has been named. Perhaps regret?). This would involve examining a_i(t;j) at some time t_0 when (i) and (j) meet (or averaging over some initial window) and then again at some later time t_1 and finally averaging over (j).

Third, one could consider the stability of a_i(t;j). It is likely that there will be some fluctuations in general. And as people grow older and their appearance changes, so may attraction. This analysis can be done by Fourier transforming a_i(t;j) over some sufficiently long interval. This interval should start long after any initial demisexuality “transient” has died out, since we’re looking for variations in the “stationary” attraction. Averaging over (j) should remove the effects of noise and extract the measure of fluidity, a global variation in attraction. Alternatively, one could also look at correlations in a_i(t;j) with a_i(t;k).

So far as I can tell, these are the only interesting identifiers that might be extracted from this model. Although one could define a great many more operators, these should suffice to denote the “sociological” orientation construct (in the sense of “Hi my name is Placeholder and I’m Arbitrary Orientation”). With a model that included more details (properties of people beyond gender, more variety in the types of interaction & attraction), we could extract more interesting correlations. But again, this is a very rough model. Perhaps you have some ideas for improving it.

As for your analogy to pitch, you are correct. Pitch is the psychological perception of sound frequency. Neural excitations become phase or mode locked to a frequency after a sufficiently long period of excitation. At higher frequencies place coding (the locations of maximum amplitude in ear) also becomes important. If you’re interested, the wikipedia article on pitch in music is a good place to start, although what you’re really looking for is psychoacoustics or psychophysics (yes, that’s a thing. Although it’s rarely included in the curriculum outside of courses for liberal arts majors, so I doubt most physicists are familiar with it.)

I think to describe a person’s attraction to people within set S (for example, S could be the set of women), you could sum a_i(t,j) over all j in S. We’ve been imagining taking a Fourier transform of a_i, but I imagine that a_i actually obeys some sort of Poisson distribution. When we talk about the frequency, perhaps we’re really thinking of the expected rate of that Poisson distribution, not the Fourier modes of the distribution. Under this interpretation, the fluidity uncertainty principle is not quite analogous to quantum uncertainty principles, but it still holds true.

I agree, Poisson statistics makes sense here, as we’re talking about infrequent events whose occurrence fluctuates about some mean waiting time. I suspect, though, that for allosexual people the Central Limit Theorem would imply a normal distribution instead. While we could still talk about (discrete) Fourier Transforms in this context, it is decidedly less useful. Uncertainty in this context is more of a classical, statistical form due to sparse information than fundamental constraints on knowledge (which isn’t to say that this sort of uncertainty is less important or significant, it plays a major role in classical chaos and non-linear dynamical systems after all). I’m unfamiliar with any sort of uncertainty principle in this context, although one could look into things like covariance and the way that limited knowledge and uncertainty propagates through various synthetic (in the sense of derived from independent parameters, rather than unnatural) properties.